Take the elevator up near the power digger wheels and head to the southwest end of the map

Important: before starting your mission, clear out all the enemies in the area around the objective marker. Do not yet activate the objective. There are primarily Field Rats and Lab Rats that can be a pain to deal with if they swarm you.

It's advisable to head north and up the ramp to the right to clear out the enemies over there as well -- otherwise you'll have to deal with them during the mission (which isn't smart, since it's a timed one)

Pull the lever at the objective marker to start the cart. A 5:00 minute timer will kick off.

Hit the switch at the next objective marker behind you. It'll close an access tunnel, forcing the cart that carries the bomb to stop in front of it.

Collect the bomb and take it to the next marker and place the bomb on it.

Head to the detonator. It's up the ramp behind you -- and then up a stairway near the building. Don't immediately use it, though.

The train will appear the moment you step in front of the detonator (regardless of how much time is left). Wait until it arrives in the middle of the bridge and stops for a second to load Eridium (you'll see the purple stuff drop into the train's cargo cars).

Hit the detonator. If you do it too early or too late, you have to run all the way back to Lynchwood to reactivate the mission.